Digital signals are transmitted through a variety of propagation paths in a wireless communication system. In addition, the digital signals are reproduced from a recording medium such as a compact disk (CD) or a digital versatile disk (DVD). The digital signals may include a variety of data errors due to noises or deformations while being transmitted and reproduced through a variety of channels.
One of techniques for correcting error is an error correction coding. The error correction coding adds extra codes to data in order to restore corrected data even when errors are included in the data.
A turbo code is one of the error correction coding. A conventional turbo code uses a duo-binary recursive systematic convolutional code for a single input. Unlike the conventional turbo code for processing an input at a time, a non-binary turbo code is introduced that simultaneously processes a plurality of inputs at a time. C. Berrou, M. Jezequel, C. Douillard, and S. Kerouedan, “The advantages of non-binary turbo codes”, Proc. Inf. Theory Workshop, Cairns, Australia, September 2001, pp. 61-63 can be referred to as an example of the non-binary turbo code.
Owing to advantages of the non-binary turbo code over the conventional turbo code, a duo-binary turbo code, which is one of the non-binary turbo codes, has been adopted as a standard in ETSI 301 790 of digital video broadcasting-return channel over satellite (DVB-RCS) and IEEE (Institute of Electrical and Electronics Engineers) 802.16-2004 section 8.3.3.2.3. In the above standards, the duo-binary turbo code is also referred to as a convolutional turbo code.
A code rate can be defined as the length of an information bit stream divided by the length of a coded bit stream. For example, if the length of the coded bit stream is 30 and the length of the information bit stream is 10, the code rate becomes one third.
The longer the information bit stream is, the longer the coded bit stream becomes, and performance of the turbo code is enhanced. If the length of the information bit stream is determined while the code rate remains the same, the length of the coded bit stream is also determined. Given the code rate, it is limited to improve performance of the turbo code.
Accordingly, there is a need to improve performance of the turbo code without increasing the length of the coded bit stream at a given code rate.